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%I #6 Oct 15 2023 18:51:28
%S 1,1,1,2,3,2,4,9,9,4,8,27,19,27,8,16,81,43,43,81,16,32,243,100,118,
%T 100,243,32,64,729,233,330,330,233,729,64,128,2187,542,923,1085,923,
%U 542,2187,128,256,6561,1260,2585,3602,3602,2585,1260,6561,256,512,19683,2929,7253
%N T(n,k) = Number of n X k 0..2 arrays with no element equal to any value at offset (-1,0) (0,-1) or (-2,-2) and new values introduced in order 0..2.
%C Table starts
%C ...1.....1....2.....4......8......16.......32........64........128.........256
%C ...1.....3....9....27.....81.....243......729......2187.......6561.......19683
%C ...2.....9...19....43....100.....233......542......1260.......2929........6809
%C ...4....27...43...118....330.....923.....2585......7253......20368.......57205
%C ...8....81..100...330...1085....3602....12102.....40901.....138307......467309
%C ..16...243..233...923...3602...14414....58775....240587.....983086.....4014830
%C ..32...729..542..2585..12102...58775...289494...1426688....7031552....34766640
%C ..64..2187.1260..7253..40901..240587..1426688...8474549...50615815...304255994
%C .128..6561.2929.20368.138307..983086..7031552..50615815..367622030..2685052098
%C .256.19683.6809.57205.467309.4014830.34766640.304255994.2685052098.23768683063
%H R. H. Hardin, <a href="/A274858/b274858.txt">Table of n, a(n) for n = 1..611</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1) for n>2;
%F k=2: a(n) = 3*a(n-1);
%F k=3: a(n) = 3*a(n-1) -2*a(n-2) +a(n-3) for n>4;
%F k=4: a(n) = 5*a(n-1) -9*a(n-2) +10*a(n-3) -6*a(n-4) +a(n-5) for n>7;
%F k=5: [order 8] for n>10;
%F k=6: [order 13] for n>15;
%F k=7: [order 21] for n>24.
%e Some solutions for n=4, k=4
%e ..0..1..0..1. .0..1..0..1. .0..1..2..0. .0..1..2..0. .0..1..2..0
%e ..2..0..1..2. .2..0..1..2. .1..2..0..1. .2..0..1..2. .1..2..0..1
%e ..0..1..2..0. .0..1..2..0. .2..1..2..0. .0..1..2..0. .2..0..1..2
%e ..1..2..0..1. .1..0..1..2. .1..2..0..1. .1..0..1..2. .0..1..2..0
%Y Column 1 is A000079(n-2).
%Y Column 2 is A000244(n-1).
%K nonn,tabl
%O 1,4
%A _R. H. Hardin_, Jul 09 2016